How do I apply gravity to a chain?
Step 1: 
To apply physics on objects you first need to go to the properties physics tab and enable rigid body on this object.





Step 2: 
If an object has to function as a hook/pin object that has to stay at its initial place, set it to Passive. 
If an object has to to function as a dynamic physics object, set it to Active.

Step 3: 
Select two of the physics objects and go to the 3D viewport physics tab. Hit connect and a new rigid body constraint empty gets generate.





Step 4: 
continue until the entire chain is connected. It should look sth like this:


 


Step 5: 
Setup the rigid body constraints of your chain.
this part needs to be tweaked to your specific needs so there is no concrete setup. But for a generic metal chain this values should be good: 





Step 6: 
 Run your animation! But make sure you have enough frames in your timeline. The physics will only get calculated to this point. if it is not enough, raise the number.